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A researcher plans a study in which a crucial step is offering participants a fo
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A researcher plans a study in which a crucial step is offering participants a fo
WEEK 8 – EXERCISES (the last one…you made it!)
Enter your answers in the spaces provided. Save the file using your last name as the beginning of the file name (e.g., ruf_week8_exercises) and submit via “Assignments.” When appropriate, show your work. You can do the work by hand, scan/take a digital picture, and attach that file with your work.
1. A researcher plans a study in which a crucial step is offering participants a food reward. It is important that the three food rewards be equal in appeal. Thus, a prestudy was designed in which participants were asked which of the rewards they preferred. Of the 60 participants, 16 preferred cupcakes, 26 preferred candy bars, and 18 favored dried apricots. Do these scores suggest that the different foods are differentially preferred by people in general? (Use the .05 significance level.)
a. Use the five steps of hypothesis testing.
b. Sketch the distribution involved.
c. Explain your findings.
2. A high school principal wanted to know if the racial makeup of her teachers mirrored that of the student body. The student body broke down into 47% White, 28% Latino, 15% African American, and 10% other. Of the 65 teachers, 42 were White, 4 were Latino, 15 were African American, and 4 were Other. Do these results suggest that the racial makeup of the faculty members is different from that of the students? (Use the .05 significance level.)
Use the five steps of hypothesis testing and explain your findings.
3. Please make up and discuss research examples corresponding to the various techniques introduced throughout this course. Describe a plausible study for each of the following statistical procedures, indicating how it would apply and what results you would predict. Also include information about the number of participants you would assess and how you would go about estimating effect size and statistical power (when relevant).
a. correlation
b. multiple regression
c. t test for independent means
d. t test for dependent means
e. ANOVA
f. chi square for goodness of fit
g. chi-square test for independence
The deadline for this assignment is 11:59 PM EST on Sunday of Week 8
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1. A researcher plans a study in which a crucial step is offering participants a food reward. It is important that the three food rewards be equal in appeal. Thus, a prestudy was designed in which participants were asked which of the rewards they preferred. Of the 60 participants, 16 preferred cupcakes, 26 preferred candy bars, and 18 favored dried apricots. Do these scores suggest that the different foods are differentially preferred by people in general? (Use the .05 significance level.)
a. Use the five steps of hypothesis testing.
b. Sketch the distribution involved.
c. Explain your findings.
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K 8 – EXERCISES (the last one…you made it!)
Enter your answers in the spaces provided. Save the file using your last name as the beginning of the file name (e.g., ruf_week8_exercises) and submit via “Assignments.” When appropriate, show your work. You can do the work by hand, scan/take a digital picture, and attach that file with your work.
1. A researcher plans a study in which a crucial step is offering participants a food reward. It is important that the three food rewards be equal in appeal. Thus, a prestudy was designed in which participants were asked which of the rewards they preferred. Of the 60 participants, 16 preferred cupcakes, 26 preferred candy bars, and 18 favored dried apricots. Do these scores suggest that the different foods are differentially preferred by people in general? (Use the .05 significance level.)
a. Use the five steps of hypothesis testing.
b. Sketch the distribution involved.
c. Explain your findings.
2. A high school principal wanted to know if the racial makeup of her teachers mirrored that of the student body. The student body broke down into 47% White, 28% Latino, 15% African American, and 10% other. Of the 65 teachers, 42 were White, 4 were Latino, 15 were African American, and 4 were Other. Do these results suggest that the racial makeup of the faculty members is different from that of the students? (Use the .05 significance level.)
Use the five steps of hypothesis testing and explain your findings.
Step 1: Research Question: Is the racial makeup of the faculty members different from that of the students?
Step 2:
Null hypothesis: = 100%
Alternative Hypothesis: NE 100%, alpha = .05
Step 3: Calculate:
Total teachers = 65
So, % White = (42/65)*100 = 65%
% Latino = (4/65)*100 = 6%
% African American = (15/65)*100 = 23%
% Other = (4/65)*100 = 6%
For a total of 100%
Step 4: Probability: 100%, all teachers reported, and student numbers are given
Step 5: Conclusion
Now, line up the numbers
Results:
White: Student % = 47%, Teacher % = 65%
Latino: Student % = 28%, Teacher % = 6%
African American: Student % = 15%, Teacher %= 23%
Other: Student % = 10, Teacher % = 6%
The racial makeup of the staff does not mirror that of the students
3. Please make up and discuss research examples corresponding to the various techniques introduced throughout this course. Describe a plausible study for each of the following statistical procedures, indicating how it would apply and what results you would predict. Also include information about the number of participants you would assess and how you would go about estimating effect size and statistical power (when relevant).
a. correlation
b. multiple regression
c. t test for independent means
d. t test for dependent means
e. ANOVA
f. chi square for goodness of fit
g. chi-square test for independence
Correlation refers to any of a broad class of statistical relationships involving dependence statistics, dependence refers to any statistical relationship between two random variables or two sets of data.
Regression analysis quantifies a relationship between a predictor variable and a criterion variable by the coefficient of correlation r, coefficient of determination r2, and the standard regression coefficient?.
Reality in the public sector is complex. There may be several possible causes associated with a problem; and likewise there may be several factors necessary for a solution. Complex statistical applications are needed which can:
-deal with interval and ratio level variables
-assess causal linkages
-forecast future outcomes
Ordinary least squares linear regression is the most widely used type of regression for predicting the value of one dependent variable from the value of one independent variable. It is also widely used for predicting the value of one dependent variable from the values of two or more independent variables. When there are two or more independent variables, it is called multiple regression.
STEPS IN MULTIPLE REGRESSIONS
The steps in multiple regression are basically the same as in simple regression.
1. State the research hypothesis.
2. State the null hypothesis
3. Gather the data
4. Assess each variable separately first (obtain measures of central tendency and dispersion; frequency distributions; graphs); is the variable normally distributed?
5. Assess the relationship of each independent variable, one at a time, with the dependent variable (calculate the correlation coefficient; obtain a scatter plot); are the two variables linearly related?
6. Assess the relationships between all of the independent variables with each other (obtain a correlation coefficient matrix for all the independent variables); are the independent variables too highly correlated with one another?
7. Calculate the regression equation from the data
8. Calculate and examine appropriate measures of association and tests of statistical significance for each coefficient and for the equation as a whole
9. Accept or reject the null hypothesis
10. Reject or accept the research hypothesis
11. Explain the practical implications of the findings
The deadline for this assignment is 11:59 PM EST on Sunday of Week 8
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